Long-range ordering of turbulent stresses in two-dimensional flow

Using filter-space techniques, we study the spatial structure of the turbulent stress that couples motion on different length scales in a quasi-two-dimensional laboratory flow. As the length scale increases, we observe the appearance of long-range, system-spanning spatial order of this stress, even though the flow field remains disordered. Suggestively, this ordering occurs only in the range of scales over which we find net inverse energy transfer to larger scales. However, we find that a field built from wave vectors with random phases also displays ordering, suggesting that at least some of the ordering we observe is purely kinematic. Our results help to clarify the role played by geometric alignment in the turbulent energy cascade and highlight the importance of the scale-dependent rate of strain in the energy-transfer process.